# List density plot for non-uniform data

I am trying to make a density plot to show the data that can found here. I tried with GNUplot previously. The result of GNUplot density plot for a rectangular set of data. I am able to do this only for a square (n x n) data set of the type:

x_1, y_1, z_1
...
x_n, y_n, z_n


where n is the number of lines.

The file that I post here is different. It is more similar to the one in the example from ListLinePlot page, which shows how to make a density plot for a spherical distribution of numbers.

Now the question is: Can I make the density plot of this data set with listdensityplot in Mathematica? The 2D map of the x-y is like that and the . As You can see all the points are in particular regions of the plot. So I expect that the density map works only in this part of the space (something simliar to this link Spreading colors in ListDensityPlot)

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d = Import["https://federico.bitrix24.com/docs/pub/10347a058a3a38a8bd8232155c080e51/?LoadFile=1"];


Using 2D binning code from that great topic it is quite fast to obtain what you need:

zvalues = Log10@d[[All, 3]];
epsilon = 1*^-10;
indexes = 1 + Floor[(1 - epsilon) 512 Rescale[d[[All, {1, 2}]]]];
SystemSetSystemOptions[
"SparseArrayOptions" -> {"TreatRepeatedEntries" -> (Total[{##}] &)}];
binmeansZ = SparseArray[indexes -> zvalues];
SystemSetSystemOptions[
"SparseArrayOptions" -> {"TreatRepeatedEntries" -> First}];

MatrixPlot[GaussianFilter[binmeansZ\[Transpose], 2], DataRange -> {{-2, 2}, {-2, 2}}]


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Is this what you are after? – Kuba May 4 '14 at 11:27
Perfect, last think: is it possible to make some smoothing of the points or not? – Panichi Pattumeros PapaCastoro May 4 '14 at 13:01
You can make not 512 but more bins and the use weider GaussianFilter. – Kuba May 4 '14 at 13:07

The example that you showed makes it clear that the plot should use a logarithmic scale. So after importing your data as a list called d, I rescale them as follows:

rescaled = {#1, #2, Log[#3]} & @@@ d;

ListDensityPlot[rescaled, InterpolationOrder -> 0, PlotRange -> All,
ColorFunction -> Hue]


There seem to be some data missing, and the plot takes a minute or so because it is very large.

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Yes in the sense that all the data is localized in a particular regions of the space and not in a rectangular form, as the graph I show to You. – Panichi Pattumeros PapaCastoro May 4 '14 at 10:46